# Properties

 Label 5808p Number of curves 4 Conductor 5808 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("5808.l1")

sage: E.isogeny_class()

## Elliptic curves in class 5808p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5808.l3 5808p1 [0, -1, 0, -10688, 404736] [2] 11520 $$\Gamma_0(N)$$-optimal
5808.l4 5808p2 [0, -1, 0, 8672, 1690240] [2] 23040
5808.l1 5808p3 [0, -1, 0, -155888, -23547456] [2] 34560
5808.l2 5808p4 [0, -1, 0, -78448, -47027264] [2] 69120

## Rank

sage: E.rank()

The elliptic curves in class 5808p have rank $$1$$.

## Modular form5808.2.a.l

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{7} + q^{9} + 4q^{13} + 6q^{17} - 4q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.